[Clear1nsight]

Change and mathematical scope

Exact finite audit and elementary norm proof: the complete cyclic observation matrices proposed in #4818, #4819 and #4826 have sharp Euclidean condition number 3 (norm 3/2 and inverse norm 2). Their reported 9/7 and 8193/8191 bounds control a loop closure factor; they do not bound the complete cascade. Invertibility and the weaker bound 16 survive.

The package also gives a concrete counterexample to using #4813's conditional plus-swap-sector cancellation on a general input: e1 produces coordinate-zero error −(1+i)/4. This describes a conditional-rule misuse, not a claim that the source asserts the conditional identity without its premise. A positive exact check confirms #4826's monomial residual factorization at its literal 32-coordinate width.

Only research/complex-block-schedule-admission-audit/ is added. No paid-call optimum, new κ or selected-frontier change follows. Actual chronological call realization, all-input ownership and restoration, raw inverse transpose, all-width lift, finite work/precision, complete caller and compiler/outer transfer remain open. Source matrix construction and injective recovery are not a priced physical word.

Task and overlap

Base 624de9dc66858af0945e5f8a0942488d62280d43; task complex-rank-shape-decoder, priority revision 7. Scope changed by explicit assignment to auditing newly proposed small-unit schedules before using their headline savings.

Audited heads: #4813 f982ecc06826e7087e69b9468d3ff52589fd0822; #4818 fd29d065bbe12f5be5af02fdf5a8b4d86dda3381; #4819 a7b42c2f8ffe5a18d305ca4dda5729d2f1d72ea8; #4826 d7b53d3992e658f0dd49d0207ba33bbc39272bac. Five unchanged source files are retained, with original Git blobs, exact hashes and immutable URLs in ORIGINS.json; no unmerged Git object is required at runtime.

Bounded live PR-body queries and all four comment timelines were checked; no comments were present. #4828's exact sharp conditioning result concerns #4743's two-bank port and explicitly excludes these cascades. #4835 concerns a characteristic-zero finite-test kernel. This work checks different concrete matrices. The heads and canonical main were refreshed unchanged at 2026-10-22 21:42 UTC. This is not exhaustive novelty or unpublished-work coverage; refresh discussions before taking the handoff.

Validation

python3 -I -B research/complex-block-schedule-admission-audit/verify.py
python3 -I -O -B research/complex-block-schedule-admission-audit/verify.py
python3 -I -B research/complex-block-schedule-admission-audit/mutation_check.py
python3 -B scripts/research_package.py --package research/complex-block-schedule-admission-audit
python3 -B scripts/check_research_commit.py --package research/complex-block-schedule-admission-audit --check-source-history

Local environment: Python 3.12.3, Linux. Exact eigenvector witnesses attain both norm bounds. Every entry of the 48- and 96-square assembled matrices and all 208 columns of the thirteen-bank forward method are compared to an independently evaluated permutation cycle. Source constructors are reused and disclosed; source bytes are authenticated before execution, and AST prefixes use those same authenticated bytes. The source's complete rank/test suites are not replayed.

Actual separate-process mutations reject a changed retained-source byte and a false new_kappa receipt in a temporary Git-free export under optimized Python. The scientific checker uses explicit exceptions. No Lean, all-size native replay, complete compiler, selected-frontier scientific replay, independent human review is claimed; hosted execution is recorded below.

Credit

Prepared for Chris R / Clear1nsight with substantial OpenAI Codex assistance, Apache-2.0. Credit hexapode for the audited proposals; Dugongue #4743, Yiyang/Lyy-iiis #4710, lee-phys #4688 and Jacob Alan Sussman #4628 for the retained construction/bound lineage. Nick Petalas #4828 addresses the distinct complete-port conditioning question. The norm method is elementary; the result is its exact application to these literal source matrices.

Open next questions

See HANDOFF.md and README. The smallest constructive next test is the chronological composition of #4813's first two overlapping native ports on actual shared banks, tracking all original inputs and charging preservation/restoration. For #4826 the earlier missing witness is a real three-call two-bank primitive containing the proposed rank-five target, with its dirty companion output and costs. A successful word then needs complete-caller pricing and funded compiler/outer transfer.

Contribution head: acd3384454083d4eb673343eb7762877d43e5394. Local registered ordinary/optimized/mutation checks and the exact committed-byte/source-history preflight passed for all 16 package files. Parent also read the proof/checker and reran the optimized scientific check successfully. Hosted CI was pending at initial publication; see the completed run below.

The latest targeted PR-body search for 4826 and cascade conditioning still returns only the original proposals, #4828 and our distinct #4839 centre-chain terminal. The bounded live handoff board was read; its loaded newest/oldest windows do not establish complete Discussion pagination. No competing exact cascade certificate was found in this inspected coverage.

Merge danger

Door: two-way. Blast radius: isolated research package. Shared implementation, frozen predecessor sources and the selected record remain unchanged.

Coordination and hosted CI

Canonical investigation and current construction claim #4843 and the required handoff identify the exact successor.

Registered research packages run 39859959815 completed successfully on exact contribution head acd3384454083d4eb673343eb7762877d43e5394, including its registered normal, optimized and actual corruption-control commands. This is bounded automated execution, not independent human acceptance, a complete paid-word realization or a new kappa.